On the Durbin-Wagle randomization device and some of its applications

Validity of Wagle's multivariate extension of the Durbin randomization device is directly proved and some vague points of the original paper are clarified. The device is then used in a non-standard way to obtain asymptotic distributions of some functions of the multivariate Gaussian sample configuration. Applications comprise, e.g., null distributions of some statistics naturally emerging in the context of invariant testing multivariate normality.